[3] He joined the front office as general manager of Jamestown in October 1984 and was promoted to assistant director of scouting in September 1985.

In 1998, owner Wayne Huizenga would order his front office to divest the team of its high-priced veterans,[7][8] and the Marlins spiraled into the basement of the National League East Division.

[11] His contentious relationship with team owner Peter Angelos began in April when the latter strongly objected to Wren's attempt to dismiss manager Ray Miller.

Wren's signings of Mike Timlin and Xavier Hernandez, the latter of which was rescinded and involved a $1.75 million settlement, were criticized by Angelos who alleged that both pitchers had been injured.

Wren's dismissal on October 7, 1999 was the result of a September 17 incident when he ordered the Orioles' chartered jet to take off without Cal Ripken Jr. who had phoned the team earlier to inform them he was going to be a few minutes late because he was stuck in traffic.

[17] In his tenure as general manager, Wren made some effective trades to acquire a resurgent Javier Vázquez in 2009, Michael Bourn in 2011, and Justin Upton in 2013.

[18] Melvin Upton joined the Braves on a 5-year, $75.25 million contract in 2013, but struggled through his two-year stint with the team[21][22] before being traded to the San Diego Padres in April 2015.

[24] The Boston Red Sox named Wren the team's senior vice president of baseball operations on September 25, 2015.

[29] His twin brother, former Georgia Tech outfielder Kyle Wren, was selected by the Cincinnati Reds in the 30th round of the 2012 MLB draft.